Paper 2022/805

Authenticated Consensus in Synchronous Systems with Mixed Faults

Abstract

Protocols solving authenticated consensus in synchronous networks with Byzantine faults have been widely researched and known to exists if and only if $n>2f$ for $f$ Byzantine faults. Similarly, protocols solving authenticated consensus in partially synchronous networks are known to exist if $n>3f+2k$ for $f$ Byzantine faults and $k$ crash faults. Currently, the only known synchronous protocol for consensus with a resilience of $n>2f+k$ is a binary consensus protocol. In this work we fill a natural gap in our knowledge by presenting MixSync, an authenticated multivalued consensus protocol in synchronous networks resilient to $f$ Byzantine faults and $k$ crash faults if $n>2f+k$. As a basic building block, we first define and then construct a publicly verifiable crusader agreement protocol with the same resilience. The protocol uses a simple double-send round to guarantee non-equivocation, a technique later used in the MixSync protocol. We then discuss how to construct a state machine replication protocol using these ideas, and how they can be used in general to make such protocols resilient to crash faults. Finally, we prove lower bounds showing that $n>2f+k$ is optimally resilient for consensus and state machine replication protocols.